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RMS - is it frequency variant?

  1. May 17, 2010 #1
    Hi folks,

    this might be a stupid question, I don't know, but I'm working on a design for a wind-driven alternator, and while calculating the rms value of the output ac, which is maximum 18Hz AC, sinusoidal, it suddenly struck me that the rms value of a low-frequency wave must surely be much lower than a high-frequency one. That is, if rms is anything like an average? I know it's not an average, but still.....

    I've looked at many sites, trying to find an equation that had a frequency or time component (and that I could understand; maths is not my strong point) but can't find anything. I'm hoping that someone here can help, or at least point me at something nearer.

    All clarifications humbly and gratefully received


  2. jcsd
  3. May 17, 2010 #2


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    No, if it is a sinewave, RMS is just 0.707 times the peak value of the sinewave and it doesn't depend on frequency.
  4. May 17, 2010 #3
    OK, thanks, vk6kro, much appreciated; however, perhaps I'm misunderstanding some exotic aspect of the meaning of root mean square; that is, if my voltage and current is cycling at say 18Hz, does it do as much work in a resistive load, as it would if cycling at 180Hz? Surely not?

  5. May 17, 2010 #4


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    There is no difference. Why do you think it should generate more heat at a higher 180 Hz instead of 18 Hz?
  6. May 17, 2010 #5


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    For a pure sinusoidal voltage source the RMS would measure the same at any frequency. In fact, the RMS value of any shape of waveform will give a measure of the power because it is the average power (V2/R), assuming the load is resistive and that VI = Power. Needless to say, you need to average over many cycles or make sure that you measure over a small number of complete cycles. Finding an instrument that will measure RMS reliably is another matter, though.
  7. May 17, 2010 #6
    I think I'm being tripped up by strict definitions of terms, maybe RMS is not what I mean, but taking an extreme case in good ol' engineering fashion, it seems that if the level was varying with a frequency of once a day or once a week the effective power, integrated over time, would be lower. So there must be a frequency component. I'll probably just finish up building an alternator and measuring the difference, if any, but I thought perhaps it was a known phenomenon, with associated equation. I've concluded that RMS is not the term or quantity that I'm looking for and that benchwork will be more useful than headscratching. I'm grateful for the opinions of the respondents, and thanks for your input. My education continues...

  8. May 17, 2010 #7


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    RMS is a very good concept although you may be looking for something different.

    If you had a big resistor and I sent you +100 volts DC for a week and then -100 volts DC for another week, the average would be zero, but you could have had your resistor running very hot for all that time. The RMS voltage would be 100 volts.

    Then if I sent you +/- 200 volts, can you see that you could have disspated 4 times as much heat in your resistor for all that time, because the power = E * E / R ?

    RMS allows for this extra heating ability for different parts of the sinewave and it also allows for the fact that negative voltages are just as effective as positive ones for heating purposes.

    The supply is varying very slowly, but the effect is the same as if you got the power at 60 Hz or any other frequency.

    Intuitively, you would think that it is harder to turn a generator fast than to turn it slowly. However, to generate the same power while turning it slowly, you would have to apply greater force to a different generator which was designed with bigger coils and bigger magnets.
  9. May 17, 2010 #8
    OK, vk6kro, thanks; I get it now - good explanation. I can relax in the knowledge that I don't need to gear up to a higher speed to achieve my ends.

    regards, ormusgold
  10. May 18, 2010 #9
    rms value of AC current is that value of a DC current that would liberate the same amount of Joule heat in a resistor.
  11. May 18, 2010 #10
    You may have to gear up.

    Running a generator at twice the frequency produces approximately twice the voltage.
    Twice the voltage is twice the power, assuming the same current.

    18 hertz is awfully slow.

    Why don't you use a car alternator and run it at say 500 RPM?
  12. May 19, 2010 #11
    As you know the rotation speed of electrical machine is related to its power supply frequency and its coupled mechanical load is function of system speed, for example the mechanical output of fans is proportional with cube of their rotation speed. Indeed the power consumption are independent of frequency just in ohmic consumers (in sinusoidal conditions).
    For similar discussion you can refer to Machine Riddle No.16 from http://electrical-riddles.com
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